Have I understood it correctly if the standard way to calculate implied correlation is the Gaussian Copula model where we:
- Calibrate the underlying portfolio to get a homogenous default probability for all assets.
- Calibrate the correlation parameter alpha to each tranche in the CDO.
I am a bit confused since the most articles i've read do not comment on the default probability, but only the correlation parameter and it seems counterintuitive to ignore one parameter.
p.s. it seems that the idea of implied correlation has been abandoned after the crash in 2008, what is a viable alternative?